A056247 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 51 for n > 0.

0, 3, 11, 15, 17, 35, 51, 71, 99, 6231, 24027, 40221, 66393

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (150*10^n - 51)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 6 followed by digit 1 is prime.

Numbers corresponding to terms <= 99 are certified primes.

Examples

			16661 is prime, hence 3 is a term.
		

References

• Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

• Patrick De Geest, PDP Reference Table - 161.
• Makoto Kamada, Prime numbers of the form 166...661.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A068647, A082700.

Programs

Mathematica

Select[Range[0, 2000], PrimeQ[(150 10^# - 51) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

PARI

a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+51)

PARI

for(n=0,1500,if(isprime((150*10^n-51)/9),print1(n,",")))

Formula

a(n) = A082700(n-1) - 2 for n > 1.

Extensions

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Edited by N. J. A. Sloane, Jun 15 2007

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Added one more term from the PDP table and a link, by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 04 2014